Magnetic perturbations

Gutowsky H S and Holm C H 1975 Time-dependent magnetic perturbations Dynamic Nuclear Magnetic Resonance Spectroscopy ed L M Jackman and F A Cotton (New York Academic) pp 1-21... 

Magnetically perturbed Mossbauer spectra of iron and tin coordination compounds. W. M, Reiff, Coord. Chem. Rev., 1973,10, 37-77 (138). 

Fig. 4.14 Magnetically perturbed quadrupole spectra simulated for powder distributions of the EFG (Vzz > 0) with an applied field B = 4T which is fixed in the laboratory system perpendicular to the y-beam/ The value of the quadrupole splitting is kept constant at AEq = +4 mm s For negative quadrupole splitting (V z < 0), the spectra would be inverted on the velocity scale. Note the difference in relative intensities for the spectrum for ry = 0 and the single-crystal type spectrum given in Fig. 4.13. Similar patterns are obtained for B y...

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

The alternative case of approximation analogous to the one mentioned above in (7.2) assumes a small magnetic perturbation and a large quadmpole interaction. This case, which is very rare and has not yet been observed in nickel systems, is expressed by the Hamiltonian [3]... 

Here, the magnetic perturbation is projected onto the quantization axes of Hq as the major interaction. 

This functional can directly be used in the DFPT equations above. Further, for the special case of a magnetic perturbation it can be shown that the response density p(1) analytically vanishes, making the calculation significantly easier. The working equations simplify to ... 

Evans, D. F. Magnetic perturbation of singlet-triplet transitions. Part III Benzene derivatives and hererocyclic compounds. J. Chem. Soc. 1959, 2753. 

The definitions of the first and second order magnetic perturbation operators are given helow. In the nonrelativistic formalism these operators are two-component operators, in the Kutzelnigg formalism all operators are to he multiplied hy the four-component matrix. All operators are given in the atomic unit system and we do not apply QED corrections so that the free electron g-factor is precisely equal to 2. 

The theory of including magnetic perturbations has been discussed earlier.(11,14-16) In Dirac theory, external fields appear through the operator... 

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

The hydrogen nucleus is classified as a Eermi particle with nuclear spin I = 1/2. Because of Pauli exclusion principle, hydrogen molecule is classified into two species, ortho and para. Erom the symmetry analysis of the wave functions, para-hydrogen is defined to have even rotational quantum number J with a singlet nuclear spin function, and ortho-hydrogen is defined to have odd J with a triplet nuclear spin function. The interconversion between para and ortho species is extremely slow without the existence of external magnetic perturbation. 

The remaining perturbed terms needed are (1) and (X+Y)j(1). We have described a methodology for obtaining these terms based on the differentiation of Eq. (40) with respect to a static magnetic perturbation (47). This approach, magnetically perturbed TDDFT, has a lot in common with the equations derived by Ortiz, van Caille and Amos and Furche and Ahrichs (70-73) that consider the RPA equation or the RPA-like form of TDDFT in the presence of a real perturbation. 

The A(0) and B(0) matrices as defined in Eqs. (41 and 42) depend on the orbital energies and several two-electron integrals collected into the elements defined in Eq. (43). The orbitals are chosen to be real. In this basis the derivatives of orbital energies with respect to a magnetic perturbation are zero. Therefore, only the derivatives of the elements are needed to evaluate A(1) and B(1). 

Evans, D. F. Magnetic Perturbation of Singlet-Triplet Transitions. Part IV. Unsaturated Compounds. J. chem. Soc. 1960, 1735. 

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